7BOBO-dHHHHHH-dH-h-7@.? - -Z`I7@.*$.6.7. $.5.7@.8.6$.6.7@.8.7@.V$.7@.xHH(FG(HH(d'@.xFHH(lA/FA--`-$*F.h9v HH-|!(}DSETBN"e-L-T-Py-v7y-vy-v y--r"y--vy--vy-,n]y-v)y-x"y-v&y-v(y-v,cy-v/oy-v1y-v46y-v6y-v9/y-x;y-v?y-vB*y-012IQRS6789STUV4567GHIJKLstuvwxyOPQRSTUV U V W 8 9 : ; < i j k l m n o p q r s t u v w x y z { | } ~       {|}~'()CDEFopq !"       &'()NOP"#$%NOPQRSTUVWXYZ[\]$%IJKLMN$%&'() Y Z [ \ ] ^ _ ` a b c               !!!!"""""##$$$$$%/%0%1%2%3%4%%%%%%%%%%%%&>&?&@&A&B&C&D&E&F&G&H&&&&'''''''''''''(( ( ( (4(5(6((((((((((((((((((((())*****+]+^+_+`+a+b+|+}+~++++,,,,,,,,, ,!,",],^,_,`,a,b,c-------.g.h.i.j.k.l......./"/#/$/%/&/'/(/)/*/+/,/g/h/i/j/k/l/m/n/o0G0H0I0J0K0L0M0N0O0000000001E1F1G1H1I1J1K1L1111111111111112G2H222223-3.3/303132333M3N3O3P3y3z3{333333333334.4/40414243444546555555555555555556k6l6m6n6o6p6q6r6s6t6u6666666666667,7-77777777778*8+8,8F8G8H8I8r8s8t888888888889'9(9)9*9+9-9.9/99:G:H:I:J:K:L::::::::::; ; ; ;z;{;|;};~;;;;;;;;;;;;;;;<<<<<<<<======= =!="=#>->.>/>0>1>2>>>>>>>>>>?????@2@3@4@5@6@@@@@@@@@@A,A-A.A/AIAJAKALAuAvAwAAAAAAAAB'B(B)B*B+B,B-B.B0B1B2B3B4B5B7B9B:B;B<B=B?BABBBCBDBEBGBHBIBJBKBLBN 9 7 L     T X            !  "  #  % ) "            Z y   > ?    c   $ $  % % % % % & ' ( +b ,c .l /o 0O 1K 33 4- 5 6 8, 9+ 9, 9- 9- 9/ 9 9 9 9 : ; < = =_ =b > ? A/ B* B+ B. B/ B0 B0 B5 B6 B7 B8 B= B> B? B@ BE BF BG BG BL BM -H-D-@ F-<E-8E-4F-0F-,X-(X-$!s- #s-'rA-*-.-2- 6b-:b-i- UNIT 9: USING RATIOS AND PROPORTIONS ODD QUESTIONS 1-39 1. A common proportion is the percentage, where a quantity is compared to 100. Suppose on your last paycheck, your gross pay was $427.50, and $51.01 was deducted for medical insurance. a. What is the ratio of medical insurance deduction to your gross pay? b. Equate this ratio to a second ratio having 100 as the denominator. What must the numerator in this second ratio be for the two ratios to be equal? c. What percentage is being deducted for medical insurance? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 3. A states automobile inspection program checks headlight alignment. The drop in the light beam cannot be greater than 2 inches for each 25 feet in front of the car. Suppose the headlights on your car are 28 inches above the ground. See the illustration below. Place illustration, page 34, here. a. What is the ratio of drop of the light beam to the distance in front of the car permitted by the inspection program? b. Suppose your headlights were adjusted to this ratio. How far in front of your car would the light beam from your headlights strike the ground? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 5. A computer desk hutch (shelves that sit atop a desk) is labeled as being 38 3/4 tall. The illustration on the box shows a fixed shelf a little more than halfway up. Your computer is 211/2 inches tall. Before you purchase the hutch, you need to know if your computer will fit under the fixed shelf. Since the height of the fixed shelf is not provided on the box, you decide to estimate the height by measuring the illustration. In the picture on the box, the hutch appears 23.2 cm tall, and the space beneath the fixed shelf is 11.4 cm. a. Would you expect the relationship between the dimensions in the picture and the real dimensions to be directly related or indirectly related? b. Write in words the ratio of the illustrations dimensions that involves the shelf height and the overall height of the hutch. Write a similar ratio in words for the real dimensions of the shelf height and hutch. c. Substitute the values you know for the words in the ratios. Since you expect the sizes in the picture to be proportional to the real sizes, set up a proportion and find the real dimensions for the shelf height. Is there enough room for your computer to fit beneath the fixed shelf? 7. Several ratios have been developed to analyze the financial strength and growth of farm businesses. One of these is the current ratio, a ratio that indicates the extent to which current liabilities could be liquidated, if necessary. Most businesses are expected to maintain a current ratio of at least 2 to 1. Current ratio = Total current assets Total current liabilities a. An analysis of the Browns farm business shows their current assets total $47,206. Their total liabilities are $9,498. Compute the Browns current ratio. b. The previous years balance sheet for the Browns showed assets totaling $38,314 and liabilities totaling $7,908. Compute the current ratio for the previous year. c. Has the Browns financial position strengthened this year (a higher current ratio) or weakened (a lower current ratio) when compared to the previous year? What are you looking for?  What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 9. The container of lawn herbicide (weed killer) instructs you to prepare a solution of 1 part full-strength herbicide to 10 parts water when using a hose-end sprayer. a. What is the ratio of full-strength herbicide to water? b. Your hose-end sprayer holds up to 16 oz of mix. If you fill the sprayer with 14 oz of water, how many ounces of full-strength herbicide should you add to obtain the proper concentration? c. Suppose for direct application, the instructions are to mix 1 oz of full-strength herbicide to each gallon of water. What is the ratio of full-strength herbicide to water in this instance? d. How does this compare to the strength of solution prepared in the hose-end sprayer? 11. A newspaper photographer took a picture of the new statue in front of city hall. The statue is 41/2 feet wide and 17 feet tall. The copy editor has room for a photograph that is 4 inches wide. a. What is the ratio of the statues width to its height? b. If the size of the photograph has this same ratio of width to height, how tall will the photograph be that fits into the width allowed by the copy editor? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 13. Inventory turnover is the ratio of the cost of goods sold to the average inventory value, as shown below. Inventory turnover = Cost of goods sold Average inventory value A ratio of 1:1 means that during the period in question the business sells an amount equivalent to the amount it stores in inventory. A smaller ratio suggests too much inventory that is not being sold. A higher value suggests a high turnover in the inventory - usually desirable for a business. Glenns Office Supplies started the year with an inventory worth $28,437, and ended the year with an inventory worth $33,010. During the year the business sold $263,841 worth of office supplies. a. Compute the average inventory value for the year, using the starting and ending values given above. b. What is the inventory turnover ratio for Glenns Office Supplies? (Round to 1 decimal place.) c. Interpret the inventory turnover ratio you obtained. Would you say that the store is a low inventory, fast turnover, or a high inventory, slow turnover business? 15. The standard aspect ratio (width to height) for a television picture is 4:3. The program director has scheduled to broadcast a wide-screen movie that was film ed with an aspect ratio of 2:1. a. Draw a sketch of a rectangular-shaped television screen on your paper that has the standard aspect ratio for a television broadcast. b. Suppose the wide-screen movie is to be broadcast so that the picture occupies the full television screen height. Draw a second rectangle on top of the first that has a 2:1 aspect and has the same height. c. Use your drawing to compute what portion of the wide screen movie pictures width will be lost at the sides. Express this portion as a percent. d. Suppose that instead of showing the full height of the movie, you wished to show the full width but maintain the correct aspect ratio of 2:1. What would be the result on the television screen? 17. As manager of a small print shop, you deal with many types of paper. You usually use international (ISO) paper sizes. Most common is the A-series used for general printed matter such as publications and stationery. The illustration below shows the relationships between the various A-series sizes, A0 through A10. The A0 size is specified to have an area of 1 m2, and measures 841 mm wide and 1189 mm long. Each successive size is half the area of the preceding size. You can obtain each size by folding the preceding larger size in half. Place drawing, page 41, here. a. What is the ratio of the width to the length, based on the dimensions of the A0 paper? b. If you were to make a single cut in the A0 paper, you would obtain two pieces of A1 paper. What would be the ratio of width to length of the A1 paper? c. Suppose you had envelopes designed to hold A2 paper. How could you fold a printed greeting card made with A0 paper to fit in the envelope? What do you think the ratio of width to length will be for the greeting card? 19. You are named as executor of a friends estate. Your friend has three children, and in his will he asks that his estate be divided among his three children in proportion to their ages at the time of his death. The amount of his estate is $107,065, and the ages of the three heirs are 52, 48, and 33 years old. a. Write the ratio of the age of each heir to the total of all their ages. According to the will, each of these ratios will be equal to a second ratio: the ratio of the amount inherited to the total estate value. b. Determine the amount each heir will inherit by solving the proportions made with the ratios of Part a. c. How can you check your calculation of each portion of the inheritance? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 21. A particular saline solution is prepared by mixing 1 part salt in 25 parts water. a. What is the ratio of salt to water in such a solution? b. If you mixed 1 part salt with 25 parts water, how many parts total would you A have? How many parts of salt are there in 100 parts of this solution? c. What percent salt is such a solution? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 23. During the first year of operation a clinic treated a total of 4836 patients, and gave 622 flu immunizations. This year the clinic is seeing many more patients. During the first six months the clinic has treated 3418, and given 481 flu immunizations. a. What is the ratio of flu shots to patients seen during the first year of the clinics operation? during the first six months of the second year? b. Regarding the amount of flu shots now being given, is the clinic giving proportionally the same number of shots, more shots, or less shots than the first year it was open? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 25. A water treatment plant deals with very large volumes of water, and very small concentrations of chemical agents. Under normal conditions, a particular chemical is added to the water to obtain a concentration of 0.9 parts per million. The treatment facility has holding tanks that contain 700,000 gallons. a. What is the desired ratio of gallons of chemical to gallons of water? b. How many gallons of this chemical should be added to the holding tank to obtain the desired concentration? What are you looking for? What do you need to answer the question?  Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 27. A standardized clothing size system has been proposed, based on metric measurements. A part of the proposal is to standardize mens shirt sizes based on the neck measurements in centimeters, as shown below. Place shirt size table, page 45, here. a. The chest size appears to increase as the neck size increases. What is the ratio of the neck size to the chest size for the smallest shirt size shown? the largest size? b. Does the ratio stay the same for all the sizes? 29. When caring for indoor plants, the proper mix of plant food is important. The label on a liquid concentrate instructs you to mix 5 ounces of concentrate in a gallon of water. a. What is the ratio (with the same units, or no units) of concentrate to water? b. Suppose you only wanted to prepare about a quart of fertilizer solution. How much concentrate should you add to a quart of water? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 31. A 2-diameter pulley is mounted on a motor shaft that turns at 1075 revolutions per minute (rpm). This pulley is connected by a belt to another pulley mounted to the shaft of a fan blade assembly. The fan pulley is 5 in diameter. Pulley diameters and speeds are inversely proportional, like gears. How many revolutions will the fan blade make each minute? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 33. A cutting oil is prepared with two oils from the stockroom, Code 171 and Code 209, in the ratio of 8 to15. a. If you started with 16 oz of Code 171, how much of Code 209 should you add? b. How many ounces total would your batch be? c. What fraction of the total batch is Code 171? Code 209? (Express your answers as percentages.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 35. A mason mixes mortar in the ratio of 1 part cement to 3 parts sand (by volume). The mixer tub can hold 0.65 m3. Each bag of cement measures about 0.05 m3. a. How much sand should the bricklayer add with each bag of cement to obtain the proper mix for the mortar? b. How many whole batches can be mixed at one time in the mixer? (One batch uses one bag of cement.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 37. A catalog lists the characteristics of several manually operated winches. One of the features listed is the gear ratio. The worm gear shown below is advertised to have a gear ratio of 41:1. That is, 41 turns of the hand crank are needed to produce one turn of the large gear. Place gear picture, page 48, here. a. The drum attached to the large gear has a diameter of 11/2 and is used to reel in a length of cable. About how many times would the hand crank have to be turned to reel in 12 of cable? (Round to the nearest whole turn of the crank.) b. Suppose you are able to turn the hand crank at a rate of 40 turns per minute. About how many minutes would it take you to wind 12 of cable? (Round to the nearest 0.1 minute.) 39. The steepness of a railroad track over a 3-mile distance is reported as a rising grade of 1 in 42. This means it rises 1 foot for every 42 feet of track. It is followed by another 5 miles of track that has a descending grade of 1 in 78. a. Which of the two distances has the steeper grade? b. How much altitude does the train gain when traveling over the first 3-mile distance? (Express your answer in feet.) c. Does the train lose all that altitude after traveling back down the following 5 miles of track? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): DSET|(H->"9 *6*>"9DSET(H-9>96*=9DSETR ----   -Unit 9 Odd Questions